Industrial Packaging & Digital Printing

Direct-to-Shape (DTS) Rotary Inkjet & Conical UV Printing Calculator

Non-linear conical frustum unwrapping, rotary surface speed compensation, and printhead droplet alignment calculator for cylindrical and tapered containers.

Process Parameters & Inputs

Container Geometry Type:

Top Diameter ($D_{\text{top}}$ in mm):

Diameter at top of active print area.

Bottom Diameter ($D_{\text{bot}}$ in mm):

Diameter at bottom of active print area (for cylinders, equals top diameter).

Print Slant Height ($H_{\text{slant}}$ in mm):

Slant length along container surface profile.

Rotary Head Resolution (DPI):

Calculated Engineering Metrics

Unwrapped Fan Arc Angle ($\theta$)

29.6degrees

Outer Arc Radius ($R_{\text{top}}$)

535.7mm

Required Vector Canvas Size

276 x 144mm

Pixel Dimension @ 720 DPI

7835 x 4082px

Toolpath & Geometry Simulation

Need Flawless DXF/SVG Contours for CAM?

SpotItLive converts technical drawings, raster graphics, and diagrams into clean, continuous vector paths ready for 5-axis CAM and CNC execution.

Convert to Scalable Vector →

Engineering Methodology & Technical Notes

Conical Frustum Unwrapping Mathematics: Direct-to-shape (DTS) rotary UV printing onto tapered drinkware, cosmetic bottles, and conical tumblers requires non-linear polar coordinate unwrapping. The flat pattern unwraps into a curved annular sector (fan shape). The vertex cone radius is $R_{\text{top}} = \frac{D_{\text{top}} H_{\text{slant}}}{D_{\text{top}} - D_{\text{bot}}}$, and the fan sweep angle is $\theta = 360^\circ \cdot \frac{D_{\text{top}}}{2 R_{\text{top}}} = 180^\circ \cdot \frac{D_{\text{top}} - D_{\text{bot}}}{H_{\text{slant}}}$.

Rotary Inkjet Drop Trajectory & Pixel Distortion: Because rotary printheads fire horizontally at a rotating tilted surface, the linear surface speed varies from top ($v_{\text{top}} = \omega R_{\text{top}}$) to bottom ($v_{\text{bot}} = \omega R_{\text{bot}}$). Vector prepress must pre-distort rectangular artwork into a polar fan shape to guarantee straight vertical lines and circular logos on the finished physical product.